Question-Answer

Question:- Prove that root n is not a rational number, if n is not perfect square Solution:- Let √n be a rational number. ∴ , where p and q are co-prime integers q≠ 0. On squaring both side we get ….(i) ⇒ n divides p² ⇒ n divides p … (ii) [If n divides p², … Read more

Question :- Prove that √2 + √5 is irrational Solution:- Let us suppose that √2 + √5 is rational. Let , where a and b coprime integers and b ≠ 0. Now Squaring both side ⇒ √2 is rational, since is rational. This contradict the fact that √2 is an irrational number. So, our assumption … Read more

Question:- Prove that √p + √q is irrational, where p and q are primes Solution:- Let us suppose that √p + √q is rational. Let √p + √q = a where a is rational number. ⇒ √p  = a – √q On squaring both side we get ⇒ [Using formula ] The above statement is a … Read more

Question:- Prove that 2 – √ 3 is irrational, given that √3 is irrational Solution: Let 2 – √3 be a rational number. Then there exist positive integers ‘a’ and ‘ b’, where a and b are integers having no common factor other than 1 and b ≠ 0 such that ⇒ Since a and … Read more

Question:- Prove that root 5 is an irrational number Solution:- Let us assume that on the contrary that √5 is a rational number. Then there exist positive integers ‘a’ and ‘ b’ such that ⇒  Where and are coprime i.e. there HCF is 1 Squaring both side ⇒ ⇒ is divisible by 5 then $a$ … Read more

Question 2: Check whether the relation R in R defined as R={(a, b): a ≤  b³} is reflexive, symmetric or transitive. Solution:-   Reflexive:- , since is not reflexive. Symmetric:- R is not symmetric.  Transitive:- is not transitive. is neither reflexive nor symmetric nor transitive. Other question:- R= {(a, b): a ≤ b²} is neither reflexive … Read more

Question 1:- Show that the relation R on the set R of real numbers, defined as R= {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive. Solution: We have, where a, b ∈ R Reflexivity:- Obiviously, is a real number and is not true. Therefore, R is not reflexive. Symmetric:- Let the real … Read more

Question:-        A and B throw a die alternatively till one of them gets ‘6’ and win the game. Find their respective probabilities of winning, If A starts first Solution:       Let S denote the success(getting a ‘6’) and F denote the failure(Not getting a ‘6’). Thus, P(A wins in the … Read more

Question:- Two balls are drawn at random one by one with replacement from an urn containing equal number of red balls and green balls. Find the probability distribution of number of red balls. Also, find the mean of the random variable. Solution:- Let X represent the number of red balls Possible value of X = … Read more